radiation pattern of a vertical dipole over sea and setup

Antonio Šarolic, Damir Senic, Zlatko Živkovic

Radiation Pattern of a Vertical Dipole over Sea and Setup forMeasuring thereof

DOI:UDKIFAC

10.7305/automatika.53-1.162621.396.674.3.08:551.4615.8.3; 3.1 Original scientific paper

In this paper, a compact setup for measuring the radiation pattern of an arbitrary positioned antenna above thesea surface is presented. The antenna of interest was a vertical half-wave dipole. Due to impracticalities concerningthe measurements using seaborne platforms, the setup was based around a shallow pool filled with actual sea water.The transmitting antenna-under-test (AUT) and the receiving antenna stands were placed on the solid ground, atthe opposite sides of the pool, thus ensuring the stable platforms as well as the wave path over sea. The need forprecise positioning of the receiving antenna along the circular path was avoided and the straight measurement linewas used instead, yielding further simplification of the method. Both antennas were realized as printed half-wavedipoles. The measurements were carried out in ISM frequency band at 2.48 GHz. The chosen frequency enabledthe realization of a compact setup for elevation radiation pattern measurements for AUT heights up to 2λ abovethe sea surface. The measurement results were compared to the theoretical and simulation results for a half-wavedipole over sea, showing a good agreement. Detailed evaluation of the measurement uncertainty was undertaken,indicating the critical points in the realized setup.

Key words: Antenna above sea surface, Lossy dielectric ground plane, Radiation pattern measurement setup, Ver-tical half-wave dipole

Dijagram zracenja vertikalnog dipola iznad mora i mjerni postav za njegovo mjerenje. U ovom radu pred-stavljen je kompaktni postav za mjerenje dijagrama zracenja proizvoljno postavljene antene iznad površine mora.Predmet analize je vertikalni poluvalni dipol. S obzirom na neprakticnost mjerenja na plovecoj platformi, postavse temelji na plitkom bazenu napunjenom stvarnom morskom vodom. Stativi za ispitivanu odašiljacku antenu iprijamnu antenu postavljeni su nacvrstom tlu na nasuprotnim stranama bazena, tako da se antene nalaze nasta-bilnim platformama, a putanja vala se nalazi u potpunosti iznad mora. Dodatna znacajka predložene metode jestpravocrtno pomicanje prijamne antene tijekom mjerenja dijagrama zracenja. Time je izbjegnuta potreba preciznogpozicioniranja po kružnoj putanji, što je dovelo do dodatnog pojednostavnjenja metode. Obje antene izra�ene sukao poluvalni dipoli u planarnoj tehnologiji. Mjerenja su provedena na ISM frekvenciji od 2.48 GHz. Odabranafrekvencija omogucuje izradu kompaktnog postava za mjerenje vertikalnog dijagrama zracenja za visine odašiljackeantene do 2λ iznad morske površine. Mjerni rezultati pokazuju dobro slaganje s analiti ckim rezultatima i rezulta-tima simulacije za poluvalni dipol iznad mora. Provedena je i prikazana detaljna procjena mjerne nesigurnosti, kaopokazatelj kriticnih tocaka u realiziranom postavu.

Klju cne rijeci: antena iznad mora, dielektrik s gubicima, uzemljena ravnina, mjerni postav za mjerenje dijagramazracenja, vertikalni poluvalni dipol

1 INTRODUCTION

The dipole antenna above a ground plane is a well-known theoretical problem [1-4] that presents the impor-tant background for many practical issues, especially inmaritime and mobile applications [5-7].

Depending on the application, the antenna height abovethe ground plane usually varies up to several wavelengths,causing the well-known lobing effect shown in [1] and[3-4]. Although the theoretical radiation characteristics

of a vertical dipole are common subject in the literature,there is evident lack of measurements performed in thereal environment, especially at sea. Analyses of such ra-diating structures are mainly based on the numerical meth-ods implemented by simulation software as a powerful toolfor solving the shipboard electromagnetic problems [8-9].However, actual measurements are of utmost importance,giving us the valuable insights into the physical phenom-ena and making possible the verification of the simulation

Online ISSN 1848-3380, Print ISSN 0005-1144ATKAFF 53(1), 56–68(2012)

56 AUTOMATIKA 53(2012) 1, 56–68

Radiation Pattern of a Vertical Dipole over Sea and Setup forMeasuring thereof A. Šarolic, D. Senic, Z. Živkovic

and/or theoretical results [10-14].

To the best of our knowledge, in available literature,there are only a few references dealing with measurementof radiation pattern of an antenna above the sea surface.The measurement setups described in literature were in-tended for specific problems and relied on considerable re-sources: in [11] the horizontal (azimuthal) radiation pat-tern was measured along the 4.6 NM long path from theship to the shore, in [12] the vertical (elevation) patternwas measured using 70-foot high wooden arch above theantenna over sea, in [13] airborne measurements were doneusing a dirigible.

The aim of this study was to produce a compact, reli-able and affordable measurement setup capable for mea-suring the radiation pattern of an antenna above the seasurface. The setup was engineered, realized and used forseveral sets of measurements, using a vertical half-wavedipole as the antenna under test (AUT). The overview ofsome preliminary results and measurement procedures hasbeen presented in [14]. This paper gives the detailed de-scription of the proposed method and the realized setup,along with the results for a set of consistent measurementscomparable to analytical results.

In section 2, the analytical solution for radiation patternof the vertical half-wave dipole above the sea surface, to-gether with the analytical and simulation results, is given.The detailed explanation of the measurement method andsetup is presented in the section 3. The measurement re-sults for the radiation pattern of a vertical half-wave dipoleover sea are presented in section 4, compared to the ana-lytical results and shown together with the boundaries ofmeasurement uncertainty. The measurement uncertainty iscalculated in section 5, where the detailed uncertainty bud-get is presented. The final remarks are given in the conclu-sion at the end.

2 RADIATION PATTERN OF A VERTICALDIPOLE ABOVE A LOSSY DIELECTRICGROUND PLANE

A vertical half-wave dipole antenna is placed in the air,alongz-axis, at a certain heighth above a lossy dielectricground plane having characteristics of sea water (Fig. 1).The analysis of the radiation pattern of a vertical dipoleantenna with the sinusoidal current distribution above aground plane can start from the well-known expressionfor the radiation pattern of an infinitesimal vertical electricdipole above a ground plane [1]:

F iϑ = sinϑ ·

∣∣ejβ0h cosϑ +Rve−jβ0h cosϑ

∣∣ , (1)

whereϑ is the elevation angle in spherical coordinate sys-tem, β0 = 2π/λ is the phase constant for free space,λ

Fig. 1. Vertical dipole above the lossy dielectric.

is the wavelength in free space andh is the height of theantenna above the ground plane.

The expression (1) is based on the pattern multiplicationrule, where sinϑ is the radiation pattern of the infinitesimalvertical dipole, and the rest of the expression represents thearray factor of a two-element array formed by the dipoleand its image below the ground plane. If a half-wave dipoleis used instead, its radiation pattern is used instead of sinϑ:

Fϑ =cos

(π2 cosϑ

)

sinϑ·∣∣ejβ0h cosϑ +Rve

−jβ0h cosϑ∣∣ . (2)

These expressions are valid in the far field, where theapproximation of parallel direct and reflected waves can beused (Fig. 1). For such approximation, Fresnel reflectioncoefficientRv for oblique incidence of a parallelly polar-ized EM wave upon a planar interface between the air anda lossy medium is defined by [1] and [15]:

Rv =η0 cosϑi − η cosψ

η0 cosϑi + η cosψ, (3)

whereϑi is the angle of incidence (for the approximationof parallel direct and reflected waves,ϑi = ϑ, as seen inFig. 1),ψ is the angle of refraction,η0 andη are the waveimpedances of the air and the non-magnetic lossy dielec-tric, respectively:

η0 =

√µ0

ε0, η =

√jωµ0

σ + jωε, (4)

whereµ0 andε0 are permeability and permittivity of freespace,σ is the conductivity andε is the permittivity of thelossy dielectric, whereε = ε0εr, (εr is the relative per-mittivity of the lossy dielectric), andω is the angular fre-quency.

AUTOMATIKA 53(2012) 1, 56–68 57


According to [15], the angleψ can be obtained as:

ψ = arctgt

q, (5)

wheret = β0 sinϑi = ω

√µ0ε0 sinϑi, (6)

q = Re {γ0} · Im {s}+ Im {γ0} ·Re {s} , (7)

while s is the complex number obtained by:

s =

√1−

(γ0γ

· sinϑi)2

, (8)

andγ0 andγ are the propagation constants in the air and inthe lossy medium, respectively:

γ0 = jω√µ0ε0, γ =

√jωµ0(σ + jωε). (9)

The electric parameters of sea water at 2.48 GHz for20◦C are taken from [16] asσ = 6.5 S/m andεr = 70.The radiation pattern calculated using (2) – (9) is given inFig. 2, for several antenna heights of interest, as the func-tion of incident angleϑi. Polar plot of the elevation radi-ation pattern of a vertical half-wave dipole ath = 2λ wascalculated using Numerical Electromagnetics Code (NEC)[17] and presented in Fig. 3.

Fig. 2. Elevation patterns calculated using (2).

3 MEASUREMENT SETUP AND METHOD

3.1 Aim and Scope

The goal of the study was to measure the vertical (el-evation) radiation pattern of the vertical half-wave dipoleTX antenna above the sea surface. Since the initial moti-vation for the study was to analyze maritime communica-tions that use vertically polarized antennas and waves, themeasurement was done specifically for the vertically po-larized component, i.e. using vertical half-wave dipole RXantenna.

Fig. 3. Elevation pattern for h = 2λ (NEC simulation using[17]).

Due to the limitations explained in section 3.4, and theprocedure explained in section 3.5, the setup is most suit-able for measuring the lower part of the elevation pattern.Considering the stated motivation, we chose to measure thepattern starting from the horizon and up to 45◦ above thehorizon, where the maritime (terrestrial) communicationactually occurs. Hence, the angles higher than 45◦ abovethe horizon were not measured.

3.2 Principles of the Measurement Setup

When considering the need for measuring the antennaradiation pattern over sea, seaborne platforms are the firstidea. However, using seaborne platforms would presentseveral serious problems to solve. The elevation patternof the AUT (antenna under test) should be measured bycontinuously varying the height of the measuring antenna.This is not easily achievable onboard a ship. Furthermore,the floating platforms do not stand still. Therefore, theinability to fine-control the TX and RX antenna positionsand polarizations would reflect in the measurement geom-etry problems. To decrease the angle error arising fromthe antenna position fluctuation, the TX and RX antennaswould have to be largely separated to a far distance. Thiswould render the pattern measurement almost impossiblefor higher angles above the horizon, because the propermeasuring antenna heights would be even more difficult toachieve. Last but not least, the flatness (or the roughness)of the sea surface should be controlled in order to prop-erly interpret the results. This is hardly achievable at seabecause there is always some kind of swell present. Evenwith no wind, there are surface fluctuations due to distantswells or, more often and unavoidable, due to ships passingby (Fig. 4).

To avoid almost all these problems, we realized thepropagation path over the sea surface using a pool filledwith sea water (Fig. 4). The precision of the TX and RXantenna positions and polarizations was secured by plac-ing their stands on the solid ground on the opposite sides

58 AUTOMATIKA 53(2012) 1, 56–68


Fig. 4. Measurement setup. No wind blowing: pool surfaceperfectly flat, sea surface not.

of the pool. The AUT was set up as the TX antenna, whilethe RX antenna was used for measurement. The flatnessof the surface was perfect in the calm conditions withoutwind.

The pool depth had to be determined to match the con-ditions at the deep sea, i.e. to be able to disregard any ef-fect of the wave transmitted beneath the sea surface. Inthe real conditions, the transmitted wave gets attenuatedfast by the lossy medium. The reflection from the sea bedis therefore irrelevant and the transmitted wave will notarise above the surface again. This eliminates any inter-ference of the transmitted wave with the incident and re-flected wave above the surface. The pool depth should beproperly determined to ensure enough attenuation.

The last issue was to determine the size of the setup,with respect to mandatory far-field conditions, consideringthe size of the antenna system (formed by the AUT and itsimage below the ground plane). The far-field requirementdetermined the pool length, while the maximum measuredelevation in the pattern was determined by the achievableheight of the measuring antenna. The former (pool length)was not as limiting factor as was the latter (measuring theantenna height). The optimum frequency had to be chosento satisfy all requirements. The pool width was not con-sidered critical and its dimension was chosen to ensure awide-enough propagation path over sea, however keepingthe setup as compact as possible.

Another practical requirement for the setup was to placeit near the sea, as to be able to fill the pool with the largevolume of sea water using a water pump. To be able toproperly control the geometry and to minimize the poolvolume, the pool had to be placed on a firm flat surface.The transmission was directed away from the land towards

the open sea. This could be useful for a directional AUT, toavoid reflections from eventual obstacles on land, but is notas important for an omnidirectional AUT. The electromag-netic requirement was to avoid any scattering objects in thevicinity of the setup. Also, the conductive material shouldbe completely avoided in the setup construction. The setupshould be easily dismountable and moveable to a chosenlocation.

3.3 Pool Depth

The pool should be deep enough to avoid the possibilitythat the transmitted wave gets reflected by the pool bottom,and appears again above the pool surface. To ensure deepsea conditions, the attenuation of the electromagnetic wavepassing twice through the 10 cm thick layer of sea waterwas calculated. The calculation was performed assumingthe worst-case scenario that includes normal incidence andtotal reflection from the pool bottom. Regarding the plane-wave propagation through a given medium, the attenuationcoefficientα is given by [15]:

α = ω√µ0ε

√√√√1

2

[√1 +

( σ

ωε

)2

− 1

], (10)

where quantities are defined as in (4). Attenuation in dBcan be calculated by:

ATT = 20 log(e2·dp·α) , (11)

wheredp is the pool depth. For the specified pool depth of0.1 m and the electric parameters of the sea water [16] at2.48 GHz (σ = 6.5S/m andεr = 70), the attenuation wascalculated to be in the range of>200 dB, which is morethan sufficient to simulate the deep sea and to neglect anyeffect of the transmitted wave.

3.4 Realization of the Measurement Setup

The overall setup dimensions were determined consid-ering the minimum necessary distance between the TX andthe RX antenna that would ensure the far-field conditions.For known wavelengthλ and the greatest overall dimen-sion of the antenna systemD, the far-field boundaryRFF

can be calculated:

RFF =2D2

λ. (12)

The antenna system (i.e. antenna array) is formed bythe original antenna and its image beneath the sea surface(ground plane). Hence, the overall dimensionD of the an-tenna system equals:

D = 2 · h+ 2 · λ4= 2 · h+

λ

2, (13)

AUTOMATIKA 53(2012) 1, 56–68 59


whereh is the AUT height above the sea surface, while2·λ/4 represents the lengths of the dipole arms that extendbeyond 2h.

The practical limit in achieving the controllable RX an-tenna height was, in our case, around 4 m. Considering thatthe goal was to measure the pattern up to the elevation of45◦ above the horizon, we decided to build a setup basedon the 4 m× 1 m pool (Fig. 5).

Fig. 5. Schematic layout of measurement setup.

The pool length defines the length of the shortest di-rect wave path, thus it should be longer than the far-fieldboundaryRFF. Considering the wavelength and (12) –(13), these pool dimensions are appropriate for measure-ments in 2.4 GHz ISM frequency band, for AUT heightsup to 1.8λ. We chose to measure at the frequency of 2.48GHz, and for the AUT heights of 0.5λ, 1λ, 1.25λ, and1.5λ. As the far-field boundary calculated by (12) is nota sharp measure, we chose to measure also for the AUTheight of 2λ.

At the defined frequency, the printed half-wave dipole(Fig. 6) was easily realized as in [18], and used as the trans-mitting and the receiving antenna.

Fig. 6. Printed half-wave dipole used for TX and RX.

The RX antenna was placed on a wooden tripod withadjustable height. The AUT holder was made of wood and

plastic, as well as all other parts of the pool and antennasupports.

Due to thickness of the pool walls (wooden boards) andthe construction details, the achieved length of the propa-gation path, i.e. the distance between the system origin andthe RX antenna, was 3.95 m.

The signal was generated by the RF signal genera-tor Rohde&Schwarz SM300 working in CW mode at2.48 GHz, and amplified by 10 W RF amplifier Ophir5140. The TX power was monitored with Rohde&SchwarzNRP-Z21 power sensor and kept constant. It is worth not-ing that the power was quite stable throughout the mea-surements and adjustments were not even needed. TheRX power was measured by the spectrum analyzer AnritsuMS2663C.

3.5 Measurement Procedure

The intuitive approach to radiation pattern measure-ment would be to measure the field along the circular patharound the AUT (shown in Fig. 7), ensuring constant ra-dius between the TX and RX antenna. However, this wouldpose significant difficulties in terms of precise positioningof the RX antenna. The RX antenna, mounted on the tri-pod, would have to pass along this curved path, measur-ing the received power at the discrete elevation angles (ac-cording to chosen angular resolution). This would implythe simultaneous adjustment of two dimensions (horizon-tal and vertical distance from the coordinate system origin,dH anddV, respectively, see Fig. 7). This procedure wastested first, and it proved to be problematic and time con-suming. Instead, we chose to measure along the verticalmeasurement line, as shown in Fig. 7. In this way, onlyone dimension,dV, had to be adjusted, whiledH was keptconstant at 3.95 m, which was far easier to achieve.

The height of the receiving antennadV had to be ad-justed to the pre-calculated discrete values, according tothe chosen angular resolution and:

dV = dH · tgδ = 3.95m · tgδ, (14)

whereδ is the elevation angle above the horizon. However,this meant that the measured RX power had to be correctedbecause it was not measured at a constant radiusr, but atthe distance increased by∆r. Since the RX power is pro-portional to1/r2, the RX power used for radiation patternmeasurement had to be corrected, i.e. increased by the fac-tor of (r +∆r)2/r2:

Pr = Pr+∆r ·(r +∆r

r

)2

, (15)

wherePr is the received power at the constant radius of3.95 m (used for radiation pattern calculation),Pr + ∆r

60 AUTOMATIKA 53(2012) 1, 56–68


Fig. 7. Geometry of the measurement setup.

is the measured received power, and∆r can be pre-calculated for angles of interest from the geometry shownin Fig. 7:

cos δ =r

r +∆r⇒ ∆r =

r (1− cos δ)

cos δ. (16)

In order to obtain the elevation radiation pattern in ac-ceptable resolution, the angle range of 45◦ was divided in15 steps of 3◦, yielding 16 measurements for every singlemeasurement procedure. The RX antenna heightdV wasmeasured using 5 m long telescopic rod equipped with alevel for control of the rod verticality.

4 MEASUREMENT RESULTS

The measurement results for the AUT heights of 0.5λ,1λ, 1.25λ, 1.5λ and 2λ are given in Fig. 8 to Fig. 12. Theresults are presented together with the boundaries of themeasurement uncertainty (expanded uncertainty, coveragefactor k = 2), which was evaluated in detail in section 5,for each AUT height.

The theoretical results were obtained for an ideal half-wave dipole over sea, using analytical relations (2) – (9),and are also shown in figures. As explained in section 3.1,all results refer to the vertical component of the electricfield, thus the analytical results were obtained by multiply-ing (2) with sinϑ.

All results were measured and presented as relative val-ues. We were not interested in the absolute values of theincident field or RX power.

To be able to compare the measured and the theoreticalradiation pattern, they should be overlapped as logically

Fig. 8. Radiation pattern for h = 0.5λ, expanded uncer-tainty (k = 2): ±4.683 dB.

Fig. 9. Radiation pattern for h = 1λ, expanded uncertainty(k = 2): ±3.776 dB.


AUTOMATIKA 53(2012) 1, 56–68 61



Fig. 12. Radiation pattern for h = 2λ, expanded uncer-tainty (k = 2): ±5.840 dB.

as possible. Since there was no absolute reference for thegraphs, first the theoretical radiation pattern was normal-ized to the maximum value, i.e. the maximum value ofthe theoretical radiation pattern became the 0 dB reference.Then the measured results in dB were compared to the pre-viously calculated normalized theoretical values for eachangle, and the mean signed absolute error was calculatedas

1

N

N∑

i=1

(xmeasuredidB − xtheoryidB

), (17)

wherexi is the result in dB atith point, andN is the num-ber of points. This mean error value in dB was applied asthe offset value to each measurement result. This resultedwith a new set of values that corresponded to the measure-ment results and still kept their relative ratios. However,the mean signed absolute error between the theoretical andthe measurement results was thus eliminated, ensuring the

most logical overlapping of two graphs in each figure.

The first point (δ = 0) was excluded from this opera-tion (thusN = 15 in (17)), since the error was too big. Thishappened because the theoretical result forδ = 0 shouldbe zero, or, in dB:−∞. However, we could not make themeasurement at exactlyδ = 0, due to finite dimensionsof the RX antenna (the RX antenna is not infinitesimallysmall). The measured result atδ = 0 thus does not refer ex-actly toδ = 0, but to the lowest point (lowest angle abovethe horizon) that could be achieved with the RX antenna,when the tip of the lower dipole arm was almost touch-ing the sea water. For this reason, the theoretical value of−∞dB is not shown on the graphs.

Graphs show that the theoretical results are in mostpoints contained within the boundaries of measurement ex-panded uncertainty with coverage factork = 2. More-over, many points overlap within±2 dB in all graphs. Theaccordance is especially good for AUT heights of 1λ and1.5λ.

It is worth noting that the stated uncertainty refers tothe realized setup and not to the proposed method in gen-eral. The uncertainty evaluation, given in section 5, showswhich particular measurements should be more precise inorder to achieve lower uncertainty.

5 EVALUATION OF MEASUREMENT UNCER-TAINTY

We proposed a novel method, realized the prototypesetup, and made the preliminary measurements. In orderto analyze the critical points in the realized setup, we havealso established the measurement uncertainty budget. Thisshould prove useful for subsequent setup realizations andmeasurements.

The evaluation was done using principles given in [19]and [20] for Type B evaluation of standard uncertainty.

5.1 Functional relationships

Individual contributions to the combined uncertaintycan be properly assessed using the mathematical functionthat expresses the dependence of the result on the mea-sured quantities. Radiation pattern measurement is basedon measurement of the received power that can be ex-pressed using the expression based on Friis equation, mod-ified according to our setup. The received power is givenby equation (all quantities in dB):

PRXdB = PTX +GTX +GRX + 10 log(

λ4π

)2 −−10 log d2 + LC +ME+ 10 log

(cos2 αTX

)+

+10 log(cos2 αRX

)+ k∆r + 10 log |F |2

(18)where:

62 AUTOMATIKA 53(2012) 1, 56–68


- PRX is the power measured by the spectrum analyzer;

- PTX is the power input to the TX antenna;

- GTX is the gain of the TX antenna,GTX = f (ϑ);

- GRX is the gain of the RX antenna,GRX = f (ϑ);

- d is the distance from the system origin to RX an-tenna;

- LC is the overall loss in connecting cables and con-nectors;

- ME is the mismatch error in the system;

- cos2 αTX is the polarization loss due to the transversal(normal) tilt of the TX antenna,αTX is the tilt angle,αTX = 0 if no tilt;

- cos2 αRX is the polarization loss due to the transversal(normal) tilt of the RX antenna,αRX is the tilt angle,αRX = 0 if no tilt;

- k∆r is the correction factor given by (15), calculatedfor each measurement point (not a measured quan-tity);

- F is the array factor of the TX antenna system.

However, the radiation pattern is given in relative terms,as the ratio (or difference in dB) between consecutivePRX power measurements for various elevation anglesϑ.Therefore, the uncertainty will be influenced only by quan-tities that can vary from one measurement to another, i.e.across the whole set of measurements. Only those contri-butions are taken into account.

5.2 Geometrical relationships

The array factorF can be considered as a superpositionof the direct and the reflected wave, i.e. the array factor ofthe two-element antenna array consisting of the AUT andits image below the ground plane:

F = 1 +Rv · e−jβ∆d, (19)

whereRv is the reflection coefficient defined by (3), and∆d is the difference in the distances traveled by the directand reflected wave (which results in the phase differencebetween the two waves). Thus, if the direct wave reachesthe RX antenna with phase 0◦, the phase of the reflectedwave shall bee−jβ∆d. Equation (19) assumes that TX gainis the same for both direct and reflected wave (whole|F |2is ultimately multiplied byGTX, i.e. added in dB in (18)).This is true if the AUT (vertical dipole) radiation patternhas its maximum pointed towards the horizon, and the

main lobe is symmetrical upwards and downwards. How-ever, if the pattern is not symmetrical (e.g. due to slightlyunbalanced feed), or if the TX antenna tilts longitudinally,the gain changes by∆GTX. The change is opposite insign for the direct and the reflected wave, as seen in Fig.13. This effect will be the greatest forϑ = 45◦ (the largestchange of gain for a tilt angle). This must be included in(19), for later estimation of the uncertainty:

|F |2 =

∣∣∣∣1 +∆GTX

GTX+

(1− ∆GTX

GTX

)·Rv · e−jβ∆d

∣∣∣∣2

.

(20)

Fig. 13. Effect of longitudinal (parallel) tilt of the TX an-tenna, for the case of uptilt.

Similar effect of gain change occurs also on the RXside, if the RX antenna is tilted longitudinally or has a non-symmetrical pattern (due to e.g. slightly unbalanced feed).Both the direct and the reflected wave arrive to the RX an-tenna from the same angle (they are approximately parallelin the far field), thus the gain change is either positive ornegative for both waves at the same time (Fig. 14).

Fig. 14. Effect of longitudinal (parallel) tilt of the RX an-tenna, for the case of downtilt.

True geometrical relationships can be observed in Fig.15. The direct wave travels the distancedd, while the re-

AUTOMATIKA 53(2012) 1, 56–68 63


flected wave travels a different distance:d1 + d2 = dr.Amplitude-wise, the difference betweendd anddr can bedisregarded and, for both waves, the distanced (from thesystem origin, point O, to the TX antenna) can be used. Itssquare, used in (18), is a function of two measured quanti-tiesdH anddV, given by:

d2 = d2H + d2V. (21)

Fig. 15. Geometry basis for phase difference calculation,without the approximation of parallel waves.

However, the difference∆d = dr − dd results inthe phase difference between the two waves described bye−jβ∆d. These quantities can be expressed by the mea-sured quantitiesh, dH anddV:

dr = d1 + d2, (22)

cos(90◦ − ϑi) =dH

d1 + d2, (23)

tg(90◦ − ϑi) =h+ dVdH

, (24)

dr =dH

cos(arctgh+dV

dH), (25)

dd =

√d2H + (dV − h)

2, (26)

∆d =dH

cos(arctgh+dV

dH)−

√d2H + (dV − h)

2. (27)

As Rv andGTX are functions ofϑi, they must be ex-pressed as functions of the measured quantitiesh, dH anddV, using (from (24)):

ϑi = 90◦ − arctgh+ dVdH

. (28)

For RX antenna in the far field,ϑ = ϑi, as seen in Fig.1.

5.3 Sensitivity coefficients

If a measurandY is determined fromN other measuredquantitiesX1, X2, . . ., XN through a functional relation-shipY = f (X1, X2, . . . , XN ), the combined standard un-certaintyuc(y) is calculated by [20]:

uc (y) =

√√√√N∑

i=1

[ciu (xi)]2, (29)

wherexi andy are the estimates of the quantitiesXi andY, respectively, andci is the sensitivity coefficient:

ci =∂f

∂xi, (30)

giving the measure of measurand sensitivity to the varia-tion of the quantityXi. When numerically calculating thevalue of the obtained partial derivative function, all argu-ments (quantities) are entered as the values measured (orcalculated) in the point of interest. If there are multiplechoices, the worst-case scenario with respect to the mea-surement uncertainty is used.

The sensitivity coefficients for quantities added in dB,as in (18), are obviously equal to 1. This is also true forquantities that are just added together into a final value,such as in distance measurements.

The sensitivity coefficient had to be calculated forthe sensitivity of d2 to quantities dH and dV, us-ing (21) and (30), for the worst-case scenario wheredH = dV = 3.95m.

As the gainsGTX andGRX are functions ofϑ (approx-imately equal toϑi, see Fig. 1 and Fig. 15), due to (28),they are also functions of the measured quantitiesh, dHanddV. Functional dependenceGTX(RX) = f (h, dH, dV)is given by the expression for the gain of half-wave dipoleand (28):

GTX(RX) =cos

(π2 cosϑ

)

sinϑ

=cos

[π2 cos

(90◦ − arctgh+dV

dH

)]

sin(90◦ − arctgh+dV

dH

) .

(31)

Therefore, sensitivity coefficients ofGTX andGRX toall three quantities were found as partial derivatives of (31)with respect toh, dH and dV, using worst-case values:h = 0.5λ, dH = dV = 3.95m.

The sensitivity of polarization loss to the normal(transversal) tilt was obtained by finding the derivative ofcos2 αTX andcos2 αRX from (18) with respect toαTX andαRX, respectively, forαTX andαRX equal to 5◦, which isthe center of the estimated interval of deviation [0◦, 10◦].

64 AUTOMATIKA 53(2012) 1, 56–68


Table 1:Expanded uncertainties for various AUT heights.

Combined standard uncertainty +/- U c 2,341 dB 1,888 dB 2,860 dB 1,425 dB 2,920 dB

Expanded uncertainty +/- 2U c 4,683 dB 3,776 dB 5,721 dB 2,850 dB 5,840 dB

h = 0.5 λ h = 1 λ h = 1.25 λ h = 1.5 λ h = 2 λ

The sensitivity ofGRX to the longitudinal tilt of the re-spective antenna was obtained by finding its derivative withrespect toϑ. Functional dependenceGRX = f(ϑ) is givenby the expression for the gain of half-wave dipole (31).The estimated interval of deviation of the longitudinal tiltwith respect to the elevation angleϑ was [0◦, 10◦] aroundthe elevation angle ofϑ = 45◦ (worst case, as explainedin section 5.2). The obtained uncertainty (i.e. the same in-terval of deviation) was used also for the calculation of TXgain change∆GTX uncertainty, as explained in (20) andin Fig. 13.

Finally, the sensitivity of|F |2 to the measured quan-tities h, dH, dV, and to the gain difference∆GTX from(20), was calculated. First, equation (20) was expressedusing (3) – (9), (27), (28) and (29), obtaining the func-tional relationship|F |2 = f (h, dH, dV,∆GTX), and thenthe respective partial derivatives were calculated for eachargument, according to (30). Due to complexity of the re-sulting equation, numerical values of the derivatives werecomputed by a mathematical software package. The worst-case scenario valuesdH = dV = 3.95m were used, to-gether with∆GTX for the estimated interval of the lon-gitudinal tilt deviation of [0◦, 10◦] around the elevationangle ofϑ = 45◦. However, the computations showed thatthe sensitivity coefficients of|F |2 heavily depend on theAUT height h. Thus, the sensitivity coefficients of|F |2were computed separately for each AUT heighth (0.5λ,1λ, 1.25λ, 1.5λ and 2λ). Accordingly, the resulting com-bined uncertainty was also calculated separately for eachAUT heighth.

5.4 Uncertainty budget

The overall expanded uncertainty is shown in Table1, separately for each AUT heighth (0.5λ, 1λ, 1.25λ,1.5λ and 2λ). The expanded uncertainty varies with AUTheight, ranging from±2.85 dB to±5.84 dB (coverage fac-tor k = 2). The detailed uncertainty budget is presented inTable 2.

The deviation intervals for all quantities were gener-ally taken as worst cases. It is also important to notethat these apply to the realized measurement setup proto-type. Subsequent setups could surely be realized with moreprecision, especially concerning the most critical quanti-ties. The largest contribution to the combined uncertaintycomes from the array factor, and the single largest con-tribution comes from the uncertainty of the AUT heightmeasurement above the sea surface. For our prototype,

we estimated the AUT height measurement deviation of±5 mm with rectangular distribution. A simulation showsthat the overall expanded uncertainty could be narrowedto ±1.5 dB to±2 dB if only the AUT height could bemeasured within±1 mm, which is achievable with moreprecise setup. Other improvements could lower the uncer-tainty down to about±1 dB (coverage factork = 2).

6 CONCLUSION

A compact and innovative setup for measuring the ele-vation radiation pattern of an antenna above the sea surfacehas been proposed, realized and tested using half-wavedipole as the antenna under test (AUT).

The choice of frequency is connected with setup sizelimits. The presented setup greatest dimension was 4 m,appropriate for the chosen frequency of 2.48 GHz and AUTheights up to 2λ above the sea surface.

The proposed setup exhibits several innovative features,such as stable TX and RX antenna platforms (while thepropagation path is still over sea surface) and straightmovement of the receiving antenna during measurements(contrary to the usual concept of measurements along thearc). Due to the latter feature, the measurements were lim-ited to the elevation angle range starting from the horizonup to a certain practical angle, 45◦ in this case. However,this range is fully adequate for most applications relatingtoterrestrial communications towards the horizon. The com-parison of the measured patterns to the analytically calcu-lated ones shows good agreement, with certain deviationsthat mainly fall within the boundaries of the calculatedmeasurement uncertainty, which ranged from±2.85 dB to±5.84 dB (depending on the AUT height above the sea sur-face). The detailed analysis of uncertainty budget showedthat further improvements are possible in terms of setupprecision, that could lower the uncertainty down to therange from±1 dB to±2 dB.

As the proposed method and setup proved their useful-ness with a well-known vertical half-wave dipole, the samemethod and setup (with possible improvements) could andwill be used for testing other types of antennas.

REFERENCES

[1] C. A. Balanis,Antenna theory, analysis and design,New Jersey, USA: John Wiley & Sons, Inc., 2005.

AUTOMATIKA 53(2012) 1, 56–68 65


Table 2:Uncertainty budget.

Value Units Distribution DivisorStandard

uncertainty

Sensitivity

coefficient

TX power measurement (constant power) 0,05 dB rectangular 1,732 0,029 1 0,029 dB

Linearity of spectrum analyzer log scale 1 dB rectangular 1,732 0,577 1 0,577 dB

Combined standard uncertainty u c(P ) 0,578 dB

Flexing (estimated) 0,2 dB rectangular 1,732 0,115 1 0,115 dB

Temperature stability (estimated) 0,15 dB rectangular 1,732 0,087 1 0,087 dB

Combined standard uncertainty u c(L c ) 0,144 dB

Scale resolution 0,0005 m rectangular 1,732 0,000 1 0,000 m

TX antenna positioning (ver. variation) 0,005 m rectangular 1,732 0,003 1 0,003 m

Combined standard uncertainty u c(h ) 0,003 m


Scale deflection 0,01 m rectangular 1,732 0,006 1 0,006 m

RX antenna positioning (hor. variation) 0,1 m rectangular 1,732 0,058 1 0,058 m

Combined standard uncertainty u c(d H) 0,058 m


RX antenna positioning (ver. variation) 0,0025 m rectangular 1,732 0,001 1 0,001 m

Combined standard uncertainty u c(d V) 0,001 m

d H 0,058 7,900 0,458 m2

d V 0,001 7,900 0,012 m2

0,459 m2

0,130 dB

TX antenna normal tilt -> polarization loss 5 º rectangular 1,732 0,050 0,174 0,009

RX antenna parallel tilt -> gain change 5 º rectangular 1,732 0,050 0,780 0,039

RX antenna normal tilt -> polarization loss 5 º rectangular 1,732 0,050 0,174 0,009

0,041

0,183 dB

h 0,003 0,121 0,000

d H 0,058 0,123 0,007

d V 0,001 0,121 0,000

0,007

0,031 dB

h 0,003 0,121 0,000

d H 0,058 0,123 0,007

d V 0,001 0,121 0,000

0,007

0,031 dB

h 0,003 137,317 0,398

d H 0,058 0,757 0,044

d V 0,001 0,758 0,001

∆G TX 0,039 1,428 0,056

0,405

2,253 dB

h 0,003 112,800 0,327

d H 0,058 0,853 0,049

d V 0,001 0,851 0,001

∆G TX 0,039 1,434 0,056

0,336

1,777 dB

h 0,003 156,977 0,455

d H 0,058 2,029 0,118

d V 0,001 2,032 0,003

∆G TX 0,039 1,437 0,056

0,474

2,788 dB

h 0,003 77,073 0,224

d H 0,058 1,845 0,107

d V 0,001 1,847 0,003

∆G TX 0,039 1,440 0,057

0,254

1,274 dB

h 0,003 154,427 0,448

d H 0,058 2,859 0,166

d V 0,001 2,865 0,004

∆G TX 0,039 1,446 0,057

0,481

2,850 dB

Uncertainty

Combined standard uncertainty u c(d2)

Combined standard uncertainty

u c(|F |2)

previously calculated u c(d H)

previously calculated u c(d V)








u c(∆G, ∆L )


u c(∆G )


u c(∆G )


u c(|F |2)







previously calculated u c(h )




= RX gain change due to parallel tilt











u c(|F |2)

Contributions to uncertainty

Power measurement, P

Cable loss stability, L c

TX antenna (AUT) height over

sea, h

Horizontal distance between TX

and RX antenna, d H

RX antenna height, d V

Distance from TX phase center to

RX antenna, squared, d2

Polarization effects on gain and

losses, ∆∆∆∆G, ∆∆∆∆L

Change in TX gain as a function

of ϑϑϑϑ determined by measured

distances, ∆∆∆∆G

Change in RX gain as a function

of ϑϑϑϑ determined by measured

distances, ∆∆∆∆G

Antenna array factor, squared

(h = 0.5 λλλλ), |F |2


(h = 1 λλλλ), |F |2


(h = 1.25 λλλλ), |F |2


(h = 1.5 λλλλ), |F |2


(h = 2 λλλλ), |F |2


u c(|F |2)


u c(|F |2)

66 AUTOMATIKA 53(2012) 1, 56–68


[2] A. De, T. K. Sarkar, M. Salazar-Palma, “Character-ization of the far-field environment of the antennaslocated over a ground plane and implications for cel-lular communication systems,” inIEEE Antennas andPropagation Magazine, vol. 52, no. 6, pp. 19-40, De-cember 2010.

[3] D. Senic, A. Šarolic, “Simulation of a shipboard VHFantenna radiation pattern using a complete sailboatmodel,” in 17th International Conference on Soft-ware, Telecommunications & Computer NetworksSoftCOM 2009,(Hvar, Croatia), pp. 1-5, September2009.

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Antonio Šarolic received the Diploma Engineer,MS and PhD degrees in Electrical Engineering in1995, 2000 and 2004 from the University of Za-greb, Croatia. He was employed at the same uni-versity from 1995 to 2005, at the Faculty of Elec-trical Engineering and Computing (FER), Dept.of Radiocommunications. In 2006 he joined theUniversity of Split, Faculty of Electrical Engi-neering, Mechanical Engineering and Naval Ar-chitecture, and is now Associate Professor inElectrical Engineering and Head of Chair of Ap-

plied Electromagnetics. His areas of interest are electromagnetic mea-

AUTOMATIKA 53(2012) 1, 56–68 67


surements, radiocommunications, electromagnetic compatibility (EMC)and biological effects of electromagnetic fields. Since 2008he has beenthe leader of the research project "Measurements in EMC and EMhealtheffects research". He is the chairman of the Croatian standardization tech-nical committees E106 "Electromagnetic fields in human environment"and E80 "Maritime navigation and radiocommunication equipmentandsystems", chairman of the IEEE EMC Society - Croatia Chapter, andmember of the Management Committee of the COST Action BM0704"Emerging EMF Technologies and Health Risk Management". He isamember of IEEE, IEICE and BEMS.

Damir Senic received the Diploma Engineer de-gree in Electrical Engineering in 2008 from theFaculty of Electrical Engineering, MechanicalEngineering and Naval Architecture, Universityof Split, Croatia. He is currently a researchassistant and PhD student at the University ofSplit, Faculty of Electrical Engineering, Mechan-ical Engineering and Naval Architecture (FESB),Department of Electronics. His research interestsare: electromagnetic measurements, bioeffects ofEM fields, electromagnetic compatibility (EMC)

and radiocommunications.

Zlatko Živkovi c received the Diploma Engineerdegree in Electrical Engineering in 2007 fromthe Faculty of Electrical Engineering, Mechani-cal Engineering and Naval Architecture, Univer-sity of Split, Croatia. He is currently a researchassistant and PhD student at the University ofSplit, Faculty of Electrical Engineering, Mechan-ical Engineering and Naval Architecture (FESB),Department of Electronics. His research interestsare: electromagnetic measurements, bioeffects ofEM fields, electromagnetic compatibility (EMC)

and radiocommunications.

AUTHORS’ ADDRESSESProf. Antonio Šarolic, Ph.D.Damir SenicZlatko Živkovi cFaculty of Electrical Engineering, MechanicalEngineering and Naval Architecture (FESB)University of SplitRu�era Boškovica 32, HR-21000 Split, Croatiaemail: [email protected], [email protected],[email protected]

Received: 2012-01-10Accepted: 2012-01-23

68 AUTOMATIKA 53(2012) 1, 56–68

radiation pattern of a vertical dipole over sea and setup

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